Mind and Context in Adult Second Language Acquisition: Methods, Theory, and Practice

2. Research Methodology: Quantitative Approaches

two Research Methodology: Quantitative Approaches rusan chen key words Chi-square test of independence ■ correlation coefficient ■ factorial ANOVA ■ goodness-of-fit test ■ hypothesis testing ■ independent-samples t test ■ multiple regression ■ normal distribution ■ one-sample t test ■ one-way ANOVA ■ paired-samples t test ■ repeated-measures ANOVA ■ simple regression. 1. Introduction A typical quantitative study includes quantification of constructs related to a research interest, data collection through experimental or nonexperimental designs, statistical data analysis, and presentation of findings related to research hypotheses. This chapter introduces commonly applied statistical procedures , with the logic of hypothesis testing as the major focus of the chapter. Hypothesis testing has traditionally been the main statistical tool used by practitioners and is still widely used by researchers in many areas, including second language acquisition (SLA). This chapter introduces statistical procedures typically covered in a one-semester introductory statistics course. It starts with an introduction of the basic concepts of statistics that serve as prerequisites to understanding the logic of statistical hypothesis testing. These concepts will be presented within contexts relevant to SLA research to facilitate SLA students’ understanding of inferential statistics. The logic of hypothesis testing will be addressed through a procedure summarized in three simple steps without mathematical derivations. This procedure will be illustrated with all statistical tests presented in subsequent sections of the chapter. The commonly used t tests, including the one-sample t test, the pairedsamples t test, and the independent-samples t test, will be introduced with numerical examples in section 3. Analysis of variance (ANOVA), including the one-way ANOVA, the factorial ANOVA, and the repeated-measures 21 ANOVA, will be introduced in section 4. Since SLA researchers frequently use the repeated-measures ANOVA with pretest, posttest, and possible delayed tests to compare different groups, this type of design will be addressed with more detail relative to other ANOVA tests. Section 5 is devoted to linear correlation and regression procedures, the methods investigating the relationships among variables. Simple regression is presented first and will provide the basis for the subsequent presentation of multiple regression, including stepwise and hierarchical regressions. Section 6 deals with the goodness-of-fit chi-square test and the chi-square test for independence . Chi-square tests are often used when the data are categorical. After learning the statistical procedures introduced in this chapter, the reader may need a guide to selecting the appropriate test for a specific research topic. As a summary of this chapter, guidelines for choosing an appropriate test based on measurement scales are presented in section 7. Due to space limitations, the introduction to each statistical procedure is kept as concise as possible, with an emphasis on conceptual understanding rather than formula derivations. In addition, some important issues, such as violation of assumptions, nonparametric tests, and power analysis for study designs, are not included in this chapter. Readers who wish to learn more about these important topics may refer to the list for further readings provided at the end of the chapter. All examples and exercises in this chapter were taken from studies recently published in SLA journals. However, the numerical data used as examples and for exercises were generated by simulation for illustrative purposes, in most cases using the means and the standard deviations presented in published articles . The SPSS (SPSS Inc. 2003, version 11.5) statistics package was used for analyzing data and presenting findings. 2. Statistics Basics and the Logic of Hypothesis Testing Most universities offer statistics courses at various levels, especially in graduate programs. Why is statistics such a popular tool that researchers in different disciplines all find it useful in their professional careers? One of the answers is that statistical procedures allow researchers to generalize the findings from their samples to the population. Researchers conducting empirical studies usually collect data from samples, but the research interests are always in the population. Using statistical procedures based on the logic of hypothesis testing, we are able to generalize the findings from the samples to the population of interest. Researchers also use statistics to summarize, present, and communicate their research findings. In this section some basic statistical concepts are introduced within the following setting. 22 theory and methodology Limited English Proficiency (LEP) is a legal term for students who are not native speakers of English and who often have trouble participating in regular classroom activities because of difficulties in speaking, understanding, reading, and writing English. According to one estimate, there are...